Berserker Prime by Fred Saberhagan
This one shows the first encounter between berserkers and Earth descended humans. Overall, its a very good story, but there's still that element of "got deadlines to meet" lingering around the edges.
SPOILER ALERT Although I think this is the best of the berserker books I've read recently, there are some items which appear flawed.
The term Goodlife was a complete surprise in the short story by that name. In this novel, ALL the data from the first encounter, including a human turncoat who used the word goodlife to describe himself, was sent to Earth and all the other colonies.
Maybe I'm wrong on this, but I had the impression the Carmpan and other non-Earth Descended branches of humanity had berserker issues before Earthlings burst on the scene. In this novel, humans are the first of all known intelligent species to be attacked.
Other stories describe the concept of a mobile atomic pile burning its way through large ships as a particularly fiendish berserker device. Somehow, the very first humans to engage in warfare after leaving the Earth use one of these against the first known berserker.
At first contact as well as the later stories (set many hundreds of years later) the technology described in the recent novels seems identical. The same "optoelectronic" computers used by both humans and berserkers. The same holostages. Nearly identical control helmets to do virtual displays for ships crews. Many of these are not mentioned in stories written earlier.
The recent novels, including this one, mention failed human attempts where intelligent von Neumann machines drift from their original purposes within 3-4 generations, thus explaining the slow reproduction rate of berserkers as being due to extreme quality control issues. A. I think it would not be hard to lock in some critical elements for a self-replicating and self-adjusting computer program. B. A strict "robot designs, builds, and writes new programs to run new robot" scheme is unnecessary for von Neumann type devices. Instead, "robot takes existing plans and builds a factory to make MANY more robots" works better. The factory, and later factories can be upgraded in what they produce, but the quality control delay would primarily apply to a brand new factory and the first of any new model being produced at any factory.
A better explanation for the entire galaxy not overflowing with berserkers would be that manufacture of berserker brains and control systems is a very delicate and slow process.
Why would a machine which had been fighting successfully (while taking massive damage from time to time) for thousands of years not try to secure additional fuel the moment its supply began to run even a little low? Instead, the refueling tankers are not deployed until after one planet is sterilized, the second had been under attack, and another human fleet arrived. Why would this same berserker not hold a single service robot in reserve to operate a device specifically able to deal with the problem of a mobile atomic pile?
One book to go.